The landscape of streaming services is a hot mess at this point...Netflix, Roku and Hulu introduced is to the phenomenon. Prices were fairly reasonable for the time... but soon, the major players learned that there was money to be made, and the race was on. The problem is that the cost of these services, while generally low ($10-ish per month, sometimes less) add up quickly, often exceeding the cost of cable tv or satellite tv services ... and each service either owns or licenses content, so the catalogs of available shows and movies can be somewhat transitional. Almost all of the major studios have their own service with their own content... so to view different shows at any given time could require multiple services.
Apple's TV+ app has their own content and also serves as an aggregator of many services, which is massively confusing... as the OP stated, much of the aggregated content is from other services and must be rented or accessed via subscriptions to those services. The interface for the TV+ app is, in my opinion, unnecessarily confusing, and just kind of vomits all over your tv screen... you have to search for the AppleTV content to see the stuff that's included without additional charge as a part of the ATV+ service.
Apple has, again, IMO, continued to perpetuate the confusion with the overlapping names for the various components.
- AppleTV, the device, is a hardware box through which you can access streaming services
- Apple TV app, the iOS and macOS app, is an app that allows you to access the streaming content on your iOS device or Mac
- AppleTC+, the service, is the catalog of streaming content provided by Apple through the AppleTV app/ AppleTV device
